A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned.
Lithography is widely recognized as one of the key steps in the manufacture of ICs and other devices and/or structures. However, as the dimensions of features made using lithography become smaller, lithography is becoming a more critical factor for enabling miniature IC or other devices and/or structures to be manufactured.
The photolithographic masks referred to above comprise geometric patterns corresponding to the circuit components to be integrated onto a silicon wafer. The patterns used to create such masks are generated utilizing CAD (computer-aided design) programs, this process often being referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional masks. These rules are set by processing and design limitations. For example, design rules define the space tolerance between circuit devices (such as gates, capacitors, etc.) or interconnect lines, so as to ensure that the circuit devices or lines do not interact with one another in an undesirable way. The design rule limitations are typically referred to as “critical dimensions” (CD). A critical dimension of a circuit can be defined as the smallest width of a line or hole or the smallest space between two lines or two holes. Thus, the CD determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit fabrication is to faithfully reproduce the original circuit design on the wafer (via the mask).
A theoretical estimate of the limits of pattern printing can be given by the Rayleigh criterion for resolution as shown in equation (1):
                    CD        =                              k            1                    *                      λ            NA                                              (        1        )            
where λ is the wavelength of the radiation used, NA is the numerical aperture of the projection system used to print the pattern, k1 is a process dependent adjustment factor, also called the Rayleigh constant, and CD is the feature size (or critical dimension) of the printed feature. It follows from equation (1) that reduction of the minimum printable size of features can be obtained in three ways: by shortening the exposure wavelength X, by increasing the numerical aperture NA or by decreasing the value of k1.
In general, the smaller the k1, the more difficult it becomes to reproduce a pattern on the wafer that resembles the shape and dimensions planned by a circuit designer in order to achieve particular electrical functionality and performance. To overcome these difficulties, sophisticated fine-tuning steps are applied to the illumination source, the projection system as well as to the mask design. These include, for example, but not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase shifting masks, optical proximity correction (OPC) in the mask layout that may include use of sub-resolution assist features (SRAF), or other methods generally defined as ‘resolution enhancement techniques’ (RET). The RET techniques that may involve modifying the design layout, may be termed as ‘optical enhancement features’ (OEF).
As discussed above, in order to shorten the exposure wavelength and, thus, reduce the minimum printable size, it has been proposed to use a radiation source that has a wavelength in the deep ultra-violet (DUV) or extreme ultra-violet (EUV) regime. While DUV wavelength regime is already commercially utilized, EUV wavelength regime is fast becoming an attractive commercial technology for the obvious reason of even shorter wavelength compared to DUV regime. EUV radiation is electromagnetic radiation having a wavelength within the range of 5-20 nm, for example within the range of 13-14 nm. It has further been proposed that EUV radiation with a wavelength of less than 10 nm could be used, for example within the range of 5-10 nm such as 6.7 nm or 6.8 nm. Such radiation is termed extreme ultraviolet radiation or soft x-ray radiation. Possible sources include, for example, laser-produced plasma sources, discharge plasma sources, or sources based on synchrotron radiation provided by an electron storage ring (especially for the x-ray wavelengths).
However, EUV lithography systems have some unique characteristics that need to be taken care of for lithographic simulation. Since EUV projection lithography systems need to rely on reflective optical elements and masks with a three-dimensional topology, as well as typically uses oblique illumination for image formation, some undesirable shadowing and flare effects arise in the lithographic process that needs to be overcome.
Flare is generally defined as the unwanted background light (i.e. noise) that is caused by scattering of light due to the roughness on the optical surfaces in the optical path. Flare degrades the image contrast at the image plane. Thus, it is desirable to reduce flare as much as possible.
The “aerial image with flare” is equal to the “aerial image without flare” convolved with a point-spread function (PSF) plus the scattering. The foregoing can be expressed as:Iflare(x,y)=Inoflare(x,y)⊗PSF+colnoflare(x,y)  (2)where Iflare is the aerial image without flare, Iflare is the aerial image with flare, and co is a conservation normalization constant that ensures cons on of energy.
In addition to the negative effect on image contrast, flare is also unevenly distributed across the scanning slit and is not uniform with the exposure field, which can cause intra-field CD variation. Therefore, protecting features and reducing background stray light becomes increasingly critical. The issue of how to reduce or negate the effects of background stray light becomes even more important as the wavelengths of the exposure tools are reduced.
Currently, a flare map is generated from a target design layout in a computational lithography-based simulation model. A flare map defines the distribution of flare within an exposure field. The flare map is generated in order to calculate the correction terms that are needed to modify the target design layout into a modified design layout for the mask. However, there is still room to improve the accuracy and efficiency of flare map generation in computational lithography, where the flare map should comprehensively incorporate the effects of mask modification (such as, addition of flare reduction assist features and/or repositioning of feature edges in the design layout) necessary to counter the optical proximity effects and other possible lithography-system-specific effects, which may modify the flare distribution.
Therefore, it is desirable to improve the accuracy of the flare map modeling, especially in DUV and EUV systems where flare effects negatively impact the imaging advantages achieved by using shorter wavelengths. At the same time, it is desirable that the accuracy of flare map modeling be achieved in a computationally efficient manner, i.e. time and computing power required to generate a flare map should be at an acceptable level within the overall lithography processing system and timeframe.